Welcome to the QuickBooks Community! Your customer list in QuickBooks Online is great way to not only keep track of who you're working with, but also their transactions by organizing them in an easy-to-access fashion. I can help you out with this.
QuickBooks Online gives you the option make customers inactive rather than completely deleting them. When you make them inactive, it removes their name from your lists so you won't accidentally create transactions for them. Here's how you can do that.
Hover over Sales in the left menu and choose Customers.
Select the arrow in the Action column for the customer in the list.
Choose Make inactive.
Since you've got a zero balance for that customer, you should have no problem making them inactive. For customers that have open balances, you'd want to address those first before making them inactive.
Another option is to simply edit that customer profile and input different information so that it's a customer you are working with. To do this, you'll want to be in the Customers section again, and this time you can click the customer name, then Edit. Simply rename the profile to something else and you won't have to worry about making the profile inactive.